A comprehensive presentation of abstract algebra and an in-depth treatment of the applications of algebraic techniques and the relationship of algebra to other disciplines, such as number theory, combinatorics, geometry, topology, differential equations, and Markov chains.
Author(s): Karlheinz Spindler
Edition: 1
Publisher: M. DEKKER, CRC PRESS
Year: 1994
Language: English
Pages: 793
City: New York
Tags: Vector Spaces, Groups
TABLE OF CONTENTS
CHAPTER 1................................................ FIRST INTRODUCTION: AFFINE GEOMETRY
CHAPTER 2 .................................................SECOND INTRODUCTION: LINEAR EQUATIONS
CHAPTER 3 ................................................VECTOR SPACES
CHAPTER 4 ......................................................................LINEAR AND AFFINE MAPPINGS
CHAPTER 5........................................ ABSTRACT AFFINE GEOMETRY
CHAPTER 6................................................. DETERMINANTS
CHAPTER 8............................................................... VOLUME FUNCTIONS
CHAPTER 9.......................................................... EIGENVECTORS AND EIGENVALUES
CHAPTER 10 ..................................................CLASSIFICATION OF ENDOMORPHISMS UP TO SIMILARITY
CHAPTER 11............................................................ TENSOR PRODUCTS AND BASE-FIELD EXTENSIONS
CHAPTER 12............................................. METRIC GEOMETRY
CHAPTER 13 ........................................................EUCLIDEAN SPACES
CHAPTER 14 ........................................................LINEAR MAPPINGS BETWEEN EUCLIDEAN SPACES
CHAPTER 15 .......................................................BILINEAR FORMS
CHAPTER 16 .......................................................GROUPS OF AUTOMORPHISMS
CHAPTER 17 ..................................................APPLICATION: MARKOV CHAINS
CHAPTER 18 .......................................................APPLICATION: MATRIX CALCULUS AND DIFFERENTIAL EQUATIONS
CHAPTER 19......................................................INTRODUCTION: SYMMETRIES OF GEOMETRIC FIGURES
CHAPTER 20 .............................................GROUPS
CHAPTER 21........................................................... SUBGROUPS AND COSETS
CHAPTER 22 ..............................................................SYMMETRIC AND ALTERNATING GROUPS
CHAPTER 23 ......................................................................GROUP HOMOMORPHISMS
CHAPTER 24 ....................................................NORMAL SUBGROUPS AND FACTOR GROUPS
CHAPTER 25 ......................................................................FREE GROUPS; GENERATORS AND RELATIONS
CHAPTER 26......................................................................GROUP ACTIONS
CHAPTER 27 .............................................GROUP-THEORETICAL APPLICATIONS OF GROUP ACTIONS
CHAPTER 28.................................................... NILPOTENT AND SOLVABLE GROUPS
CHAPTER 29................................................. TOPOLOGICAL METHODS IN GROUP THEORY
CHAPTER 30............................................... ANALYTICAL METHODS IN GROUP THEORY
CHAPTER 31............................................... GROUPS IN TOPOLOGY
